Theoretical analyses and optimizations for wavelength conversion by quasi-phase-matching difference frequency generation

Under the undepleted-pump approximation, the conversion efficiency η and bandwidth Δλ based on quasi-phasematching (QPM) difference frequency generation (DFG), are theoretically studied in detail and their expressions are obtained. The theoretical results show that, for the uniform grating, η logarithmically increases with L, whereas Δλ decreases under the perfect phase matching. Contrarily, when η reaches the minimum, the bandwidth Δλ, which is independent of the second-order nonlinearity, the pump, and the signal power, reaches the maximum under the imperfect phase matching. The expression of η for the arbitrary chirp QPM grating in the typical DFG process is obtained in this paper for the first time. Optimized examples for two-, three-, and four-segment chirp grating are given, respectively. The numerically optimized results show that both the pump and signal bandwidth Δλ can apparently be widened in the chirp grating although η may decrease a little, and that, with the adding of segment numbers, Δλ can increase